All Questions
Tagged with fourier-transform time-series
77 questions
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Why is Prophet faster than dynamic harmonic regression?
Section 12.2 of Forecasting: Principles and Practice (3rd edition) discusses Facebook's Prophet model. The authors write:
Prophet has the advantage of being much faster to estimate than the [dynamic ...
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9
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Help with PSD graph interpretation and Time Series Analysis
I am pretty new to time series analysis and I am currently studying it. My latest work requires me to work with a time series that was generate by VASP AIMD. I tried power spectrum density analysis ...
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14
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What is the spectral density matrix, in the context of vector stochastic processes
I cannot seem to find any good/easy to read resources on the spectral theory, and in particular for multivariate stochastic processes.
I want to know:
Any resources explaining spectral theory
...
- 379
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33
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Forecasting Square Waves
I am involved in a social experiment with other college students. The experiment involves simulating current price of the market at which a given asset can be bought or sold for immediate delivery. We,...
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31
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Approximation for a correlation matrix
I have a cross-correlation matrix of some parameter for each time period. E.g. expected economy growth for each months in the future, i.e. growth for Apr 2014, May 2014, ...., Dec 2018, and ...
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49
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Fourier coeficients as feature to classification model
I have to solve a timeseries multiclass classification problem. Some of these classes (Class 0, Class 1 and Class 4) have timeseries that are really similar to each other, as follows:
...
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48
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Energy of a signal contained within a given band
Suppose I wish to compute the energy contained in a given frequency range using FFT. So, first, I compute FFT and take the squares of the absolute values of $x_k$. Can I then use discrete integration ...
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Is it possible to have seasonality at 24, 12, 8 periods in hourly based wind power data?
I have taken hourly-based wind power data, by taking its periodogram after making it stationary in R. It gives me four seasonal patterns at periods of 24, 12, 08, and 06, as shown in the figure below.
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63
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Can regression forecasts of univariate time series be independent (of one another)
Suppose I have short-term forecasts from two univarite regression models of the same time series. I am choosing the models to be as different as possible in structure and assumptions. For instance, ...
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475
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How to calculate harmonic equations from a complex wave
I’m working through an online example that explains spectral analysis in R. Let’s say you have a complex wave:
...
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45
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Periods of High Activity Detection
So I have some sensor data (time series) of heart rate of some users. I want to detect the times they start and finish exercising.
The data is sensor readings of heart rate every second, it's ...
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The length of spectral density is longer than the data using spectrum() in R
I'm using spectrum(method = "pgram") in R to calculate the spectral density in my time series.
spectrum() returns the spectral density for each frequency(from 1/n, 2/n to 1/2, n is the time ...
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Using Fourier Coefficients to approximate a time series
I'm trying to understand approximating periodic functions with Fourier Transforms. I'm using R, but I suppose the question is language agnostic.
Say I have this discrete periodic series. It is some ...
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1
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406
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Seasonal ARIMA vs ARIMA with Fourier terms for monthly series
I have monthly data and my goal is to forecast values with an inclusion of exogenous variables. I've built SARIMA and Dynamic Harmonic Regression models, where the second one performs little bit ...
- 511
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Looking for repeated patterns in time series data
I have spent the best part of the last few days searching forums and reading papers trying to solve the following question. I have thousands of time series arrays each of varying lengths containing a ...
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How to identify a non-periodic time-series?
I am working on a problem where I have to first classify whether a time-series is periodic or not and then, if it is periodic identify its period(s) (the time-series could have multiple periodicities, ...
- 275
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103
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Finding autocorrelation coefficients given PSD values at 2 frequencies
Assuming that $S_X(w)$ denotes powers spectral density function at
frequency $w$, we are given
$$S_X\left(\frac{\pi}{4}\right)=10+3\sqrt{2},\quad
S_X\left(\frac{\pi}{6}\right)=11+3\sqrt{3}.$$ We also ...
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2k
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Model specification for seasonal ARMA-GARCH model using rugarch
TL;DR: I'm trying to find an adequate model for time series data that exhibits multiplicative seasonality and volatility clustering by identifying an ARMA-GARCH-model with Fourier terms using ...
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151
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Using Cross Validation for Highly Seasonal Data with small sample
I'm having trouble getting good scores on cross validated metrics on time series regression models. Essentially, I am trying to model product purchases based on amount of money spent on different ...
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1
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254
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Estimating Fourier spectrum from multiple time series of a system
I have a set of N time series, each of length T, that describe separate realisations of a single physical system. For each series, I can compute an FFT to find the Fourier spectrum up to a period 2/T, ...
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181
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Spectral analysis in R, how to interpret periodogram
I'm relatively new to spectral analysis and have been working through some online tutorials. I have some time series data that I would like to examine for periodicity / repeating patterns.
When I ...
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1
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2k
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Why SARIMA has better accuracy on weekly dataset than on daily one?
I am studying time series right now. So, I have this dataset. My aim is temperature prediction.
I've found out that ARIMA can't work with long period seasonality. So, I've resampled daily dataset ...
- 160
1
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146
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Log-likelihood function for a filtered Fourier spectrum
I have time series data from which I am trying to infer parameters using MCMC. I normally infer parameters about the data in the time domain, using a Normal log-likelihood. However, I now have to ...
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221
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How to search for irregular signals: Fourier, DWT or k-means?
See my notebook here
I want to search for irregular time signals in a data set of ~3 500 000 time signals. I can't give a clear definition of irregular signal, but it must fulfil the criteria of: not ...
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812
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Why is spectral density only defined for stationary processes?
I read Brockwell and Davis(2016), Shumway and Stoffer(2016), and Stoica and Moses(2004). However, none of them laid out clearly the reasoning behind the presumption of stationarity when conducting ...
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2k
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K in Fourier series - How to find value of K to use it in ARIMA?
I am using the forecast library for doing some time series forecasting. I need to forecast number of sold items. I am planning to add holidays as xreg in auto.arima. The holiday will be a 0/1 list, ...
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1
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192
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Continuous time Fourier representation
I have learned that the Fourier transform of a continuous-time unit-periodic stochastic process is:
$$x(t) = \sum\limits_{k=-\infty}^{\infty} a_k e^{i2\pi kt} \quad \quad \text{ where } \quad \quad ...
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2
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2k
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Inverse Fast Fourier Transform in R
plot(fft(fft(1:100),inverse = "true")/100)
plot(1:100)
In the above example, I was expecting the plots to be identical.
The first, however, returns:
while the ...
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394
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Frequency analysis of categorical/binary data
I want to do frequency analysis with a data set of consecutive binary values, such as "Rainy - Sunny - Rainy - Rainy - Rainy - Sunny - ...". Using this data, I want to extract the frequency (= the ...
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Maximum number of Fourier terms in forecast package
I am using the forecast package in R to get some Fourier components - namely, function fourier(ts, K, ..). For a time series <...
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679
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How to fit a model to both daily and weekly periodic data using linear regression and fourier transform
I have a variable, y, in 30 minute intervals, and is highly dependent both on the time of day and the day of the week - mainly Sundays. It is also dependent on bank holidays, which could by any day of ...
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336
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Fourier Output Meaning
I just ran a fourier series on weekly sales data for 3 years worth of data.
I optimally chose the number of k-terms based on the AIC.
First 6 lines of my data:
...
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340
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Need help understanding output of a periodogram
In my effort to understand the output of a periodogram I created a series (s) where 1,1,1,1,1,1,1,1,1,10 is repeated 100 times and then created a periodogram of this series using the following R code:
...
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Forecasting with ARIMA ( Training and Test Data split)
I have an hourly time series of the average parking occupancy with data available from September 2017 up until June 2018. I would like to use the ARIMA model with external regressors to produce a ...
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716
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Calculating right values of Periodogram using Fourier Analysis
In the book, Economic Cycles: There Law and Cause By Henry Ludwell Moore, he plots Periodogram of rainfall of Ohio valley. He uses 72 years data (1839-1910) and tries to find the most dominant cycle ...
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2k
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Proof of Herglotz Theorem in Time Series Analysis
I am studying time series, following Time Series Theory and Methods by Brockwell and Davis. I am reading the proof of the Herglotz Theorem, I have the following questions.
First, the proof given in ...
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258
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Spectral density and Riemann Stieltjes Integral
I am confused with a part about spectral densities. I found it in Time Series Theory and Methods by Brockwell and Davis.
I don´t understand how is applied the Riemann Stieltjes Integral in this ...
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2
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269
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Is this a well-studied problem? Problem: Optimally unlagging multiple time-series
Is the problem of optimally lagging/unlagging multiple time-series with integer lags to maximize a sum of pairs of cross correlations or coherence an already well-studied problem? If so, references? ...
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Power spectral density of the output of a linear time invariant system with a weakly-stationary process
Please note that I have no background whatsoever in Fourier analysis and very little in time series.
This is exercise 2.10 in Theodoridis' Machine Learning:
Show that the autocorrelation of the ...
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4k
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Spectral Analysis in R - the periodogram
I am doing a spectral analysis in R using the spec.pgram() function. Suppose I have observations for $y_1$ to $y_n$ which are a time series with annual observations....
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516
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Generating time series for electricity demand
I'm working on a project, trying to model electricity consumption and generation from a bunch of PV generators to see how much of the demand can be satisfied by the production in the "town".
Most ...
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2
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3k
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Dealing with multi seasonality in time series
I am new in R and time series analysis and need some help. I am currently trying to create a tool to forecast the demand of power for a company. On my data set I have 17550 observations that ...
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4k
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Finding out frequency of peaks using the Fourier transform
I have a signal that varies in time as shown below. I have just shown a 5 s interval of data (from 97 s to 102 s). The sampling frequency is 1000 Hz.
My goal is to find out the frequency of the ...
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How to measure a mean frequence of fft transform
I have this time series (utilization of app by day of an user)
And this fourier transform of the above time series
How can I extract one number that express the mean frequency of this time series?
...
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334
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Energy savings prediction model using stochastic processes and Monte Carlo Simulation
I want to build a model that quantifies the energy savings from a building retrofit project. For example a company is using a heating oil radiator system, that is meant to be replaced by a gas ...
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229
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detecting change point in the time series on a 2 dimensional space
I have a 2 dimensional geographic space. There are crime events occuring at different regions in the space over time. I am looking particularly at property crimes like burglary. If I look at the time ...
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The small error probability P for a dataset
P = $p\{\frac{|\epsilon(k)-\bar{\epsilon}|}{S_1} < 0.6745\}$
Say we want to calculate the probability shown in the formula above.
I have the values for all $\epsilon$ parameters and $S_1$. ...
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429
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Fourier Transform-Time stamped data and Linear Regression
I am new to DFT (Discrete Fourier Transform), but I am trying to use it to decompose my traffic volume data into two vectors (x,y i.e. independent and dependent variables). Afterwards I can apply a ...
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428
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'Arima + fourier' for periodic data Improvement Suggestions
On the plot black is the data and red are the fitted values obtained from fitted i.e. one step forecast, I am using 365 days for training and then 3000+ days for ...
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Deseasonalizing data with fourier analysis
I have a data which has two underlying behavior. First there is a periodicity in it. It looks like a sine curve. Secondly the data points have constant growth in it. So, if I have 100 data points ...
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